Having a power of attorney for nursing home patients and nursing home bills is a good idea but the power of attorney is not personally responsible for paying the nursing home bills.
Having a power of attorney helps to ensure that day to day financial affairs will be handled in the case of the persons incapacity where they're unable to make those decisions.
Still the nursing home bills are required to be paid from the patients assets or other insurance but the power of attorney is not responsible for paying the nursing home bills but just making sure that the nursing home bills are paid from the insurance or assets.